Compactly supported wavelets with dilation factor a = 3
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Date
1993
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Abstract
It is well known that any compactly supported orthonormal (o.n.) wavelet which is symmetric or antisymmetric is some integer-translate and possible sign change of the Haar function. Here, the scaling factor a = 2 is used to define the wavelets. However, when wavelets are used for signal or image analysis, for instance, it is very important to avoid phase-distortion; and this requires symmetry or antisymmetry of the wavelet functions. One of the objectives of this thesis is to investigate the construction of compactly supported o.n. symmetric scaling functions with scaling factor a = 3 and the two corresponding compactly supported o.n. wavelets, one of which is symmetric and the other antisymmetric. Examples of low-order scaling functions and wavelets are given. Moreover, we exhibit some additional desirable properties of semi-orthogonal (s.o.) wavelets. In this regard, we emphasize on cardinal B-spline functions and obtain their corresponding symmetric and antisymmetric wavelets, which have the same supports as the corresponding cardinal B-splines. Furthermore, because of the close connection between the notion of subdivisions and scaling functions, we develop some new subdivision schemes.
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Vita.
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Major mathematics